(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 131314, 4529]*) (*NotebookOutlinePosition[ 132493, 4571]*) (* CellTagsIndexPosition[ 132418, 4565]*) (*WindowFrame->Normal*) Notebook[{ Cell["Thermal Transport Cross Sections for He -He Collisions", "Subtitle"], Cell[CellGroupData[{ Cell["Setup notebook environment", "Text"], Cell["ClearAll[\"Global`*\"]; ", "Input"], Cell["Remove[\"Global`*\"]; ", "Input"], Cell["startclock = SessionTime[];", "Input"], Cell["Off[General::spell]", "Input"], Cell["Off[General::spell1]", "Input"], Cell["Off[NumberForm::sigz]", "Input"], Cell["<< Graphics`Graphics`", "Input"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(now\ = \ StringForm["\<``/``/`` ``:``:``\>", \(Date[]\)[\([2]\)], \(Date[]\)[\([3]\)], \(Date[]\)[\([1]\)], \(Date[]\)[\([4]\)], \(Date[]\)[\([5]\)], \(Date[]\)[\([6]\)]]\)], "Input"], Cell[BoxData[ InterpretationBox[ "\<\"\\!\\(8\\)/\\!\\(24\\)/\\!\\(1998\\) \ \\!\\(22\\):\\!\\(38\\):\\!\\(56\\)\"\>", StringForm[ "``/``/`` ``:``:``", 8, 24, 1998, 22, 38, 56], Editable->False]], "Output"] }, Open ]], Cell["\<\ We wish to determine the viscosity and momentum transfer cross sections for \ He in He from calculated thermal viscosity and diffusion data, e.g., Saxena, \ High temp. Sci. 3, 168 (1971). We use this reference primarily because it is \ convienient, rather than because we have done a review of the experimental \ literature. We consider diffusion first because it is more familiar to us \ than viscosity.\ \>", "SmallText"], Cell["Momentum transfer or diffusion cross section", "Section"], Cell["\<\ It should be kept in mind that the theory of self diffusion is messy. \ However, my reading of Chapman and Cowling, Sect. 14.5 is that in the end one \ uses the theory for mixed gases with equal mass.\ \>", "SmallText"], Cell["Input data", "Subsection"], Cell["\<\ The results can be expressed in terms of self-diffusion coefficients versus \ temperature. \ \>", "SmallText"], Cell["\<\ From Chapman and Cowling, p. 267 the self-diffusion coefficient at NTP is \ 1.56 cm^2/s so that the normalized diffusion coefficient is 3.87 *10^21 \ m^-1s^-1.\ \>", "SmallText"], Cell["\<\ ccnormdifflistplot = LogLogListPlot[{{296,3.87}}, PlotRange -> {{100,10000},{0.1,10}}, PlotStyle -> PointSize[0.02], DisplayFunction -> Identity];\ \>", "Input"], Cell["The slope comes from viscosity data as r = 0.66.", "SmallText"], Cell[BoxData[ \(\(r\ = \ 0.66; \)\)], "Input"], Cell["empnormdiff = 8.85*(temp/1000)^r; (*10^19 m^-1s^-1*)", "Input"], Cell["\<\ empnormdiffplot = LogLogPlot[empnormdiff, {temp,100,10000}, PlotRange -> {1,100} , DisplayFunction -> Identity];\ \>", "Input"], Cell[CellGroupData[{ Cell["\<\ Show[empnormdiffplot,(*normdifflistplot,*)ccnormdifflistplot, DisplayFunction -> $DisplayFunction];\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.928573 0.476191 0 0.309017 [ [.02381 -0.0125 -11 -12.875 ] [.02381 -0.0125 11 0 ] [.16716 -0.0125 -11 -12.875 ] [.16716 -0.0125 11 0 ] [.35665 -0.0125 -11 -12.875 ] [.35665 -0.0125 11 0 ] [.5 -0.0125 -14 -12.875 ] [.5 -0.0125 14 0 ] [.64335 -0.0125 -14 -12.875 ] [.64335 -0.0125 14 0 ] [.83284 -0.0125 -14 -12.875 ] [.83284 -0.0125 14 0 ] [.97619 -0.0125 -17 -12.875 ] [.97619 -0.0125 17 0 ] [-0.0125 .09302 -10 -6.4375 ] [-0.0125 .09302 0 6.4375 ] [-0.0125 .21599 -10 -6.4375 ] [-0.0125 .21599 0 6.4375 ] [-0.0125 .30902 -16 -6.4375 ] [-0.0125 .30902 0 6.4375 ] [-0.0125 .40204 -16 -6.4375 ] [-0.0125 .40204 0 6.4375 ] [-0.0125 .52501 -16 -6.4375 ] [-0.0125 .52501 0 6.4375 ] [-0.0125 .61803 -22 -6.4375 ] [-0.0125 .61803 0 6.4375 ] [ -0.0005 -0.0005 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid .02381 0 m .02381 .00625 L s gsave .02381 -0.0125 -72 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (100) show 81.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .16716 0 m .16716 .00625 L s gsave .16716 -0.0125 -72 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (200) show 81.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .35665 0 m .35665 .00625 L s gsave .35665 -0.0125 -72 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (500) show 81.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .5 0 m .5 .00625 L s gsave .5 -0.0125 -75 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (1000) show 87.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .64335 0 m .64335 .00625 L s gsave .64335 -0.0125 -75 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (2000) show 87.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .83284 0 m .83284 .00625 L s gsave .83284 -0.0125 -75 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (5000) show 87.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .97619 0 m .97619 .00625 L s gsave .97619 -0.0125 -78 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (10000) show 93.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .001 w .25101 0 m .25101 .00375 L s .3105 0 m .3105 .00375 L s .39436 0 m .39436 .00375 L s .42624 0 m .42624 .00375 L s .45385 0 m .45385 .00375 L s .47821 0 m .47821 .00375 L s .7272 0 m .7272 .00375 L s .7867 0 m .7867 .00375 L s .87055 0 m .87055 .00375 L s .90243 0 m .90243 .00375 L s .93004 0 m .93004 .00375 L s .9544 0 m .9544 .00375 L s .25 Mabswid 0 0 m 1 0 L s 0 .09302 m .00625 .09302 L s gsave -0.0125 .09302 -71 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (2) show 69.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .21599 m .00625 .21599 L s gsave -0.0125 .21599 -71 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (5) show 69.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .30902 m .00625 .30902 L s gsave -0.0125 .30902 -77 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (10) show 75.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .40204 m .00625 .40204 L s gsave -0.0125 .40204 -77 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (20) show 75.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .52501 m .00625 .52501 L s gsave -0.0125 .52501 -77 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (50) show 75.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .61803 m .00625 .61803 L s gsave -0.0125 .61803 -83 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (100) show 81.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .001 w 0 .14744 m .00375 .14744 L s 0 .18605 m .00375 .18605 L s 0 .24046 m .00375 .24046 L s 0 .26115 m .00375 .26115 L s 0 .27907 m .00375 .27907 L s 0 .29488 m .00375 .29488 L s 0 .45646 m .00375 .45646 L s 0 .49506 m .00375 .49506 L s 0 .54948 m .00375 .54948 L s 0 .57017 m .00375 .57017 L s 0 .58809 m .00375 .58809 L s 0 .60389 m .00375 .60389 L s .25 Mabswid 0 0 m 0 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .08867 m .35732 .23151 L .48712 .2871 L .56221 .31927 L .61532 .34201 L .65999 .36115 L .69545 .37633 L .72746 .39004 L .75423 .40151 L .77707 .41129 L .79889 .42064 L .81793 .42879 L .83471 .43598 L .8512 .44304 L .86592 .44934 L .8805 .45559 L .89363 .46121 L .90552 .46631 L .91747 .47142 L .92835 .47608 L .93932 .48078 L .94936 .48508 L .95859 .48904 L .96797 .49305 L .97619 .49657 L s .02 w .24823 .18161 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggoool001Woool00`000?ooooooo`0Goooo0P000>_oool001Woool00`000?ooooooo`0Ioooo0P00 0>Woool001Woool00`000?ooooooo`0Koooo0`000>Koool001Woool00`000?ooooooo`0Noooo0P00 0>Coool001Woool00`000?ooooooo`0Poooo0`000>7oool001Woool200009?ooo`80003Ooooo000I oooo00<0003oooooool09Oooo`80003Moooo000Ioooo00<0003oooooool09oooo`<0003Joooo000I oooo00<0003oooooool0:_ooo`80003Hoooo000Ioooo00<0003oooooool0;?ooo`80003Foooo000I oooo00<0003oooooool0;_ooo`<0003Coooo000Ioooo00<0003oooooool0?ooo`H00036oooo000Ioooo0P00 03[oool50000a_ooo`006Oooo`030000oooooooo03[oool50000aOooo`006Oooo`030000oooooooo 03ooool20000`oooo`006Oooo`030000oooooooo047oool30000`?ooo`006Oooo`030000oooooooo 04Coool20000__ooo`006Oooo`030000oooooooo04Koool20000_?ooo`004?ooo`800007oooo00<0 003oooooool0B?ooo`<0002ioooo000?oooo00@0003oooooool00006oooo00<0003oooooool0Booo o`80002goooo000Boooo00<0003oooooool01?ooo`<0001=oooo0`000;Coool0013oool200001ooo o`030000oooooooo053oool20000/_ooo`004?ooo`030000oooooooo00Koool00`000?ooooooo`1B oooo0P000;3oool0013oool300001_ooo`030000oooooooo05Coool30000[Oooo`006Oooo`030000 oooooooo05Ooool20000Zoooo`006Oooo`030000oooooooo05Woool20000ZOooo`006Oooo`80001L oooo0`000:Koool001Woool00`000?ooooooo`1Noooo0P000:Coool001Woool00`000?ooooooo`1P oooo0P000:;oool001Woool00`000?ooooooo`1Roooo0`0009ooool001Woool00`000?ooooooo`1U oooo0P0009goool001Woool20000J?ooo`<0002Joooo000Ioooo00<0003oooooool0J_ooo`80002H oooo000Ioooo00<0003oooooool0K?ooo`80002Foooo000Ioooo00<0003oooooool0K_ooo`<0002C oooo000Ioooo0P0007;oool20000TOooo`006Oooo`030000oooooooo07?oool20000Soooo`006Ooo o`030000oooooooo07Goool30000S?ooo`006Oooo`030000oooooooo07Soool20000R_ooo`006Ooo o`80001koooo0P0008Soool001Woool00`000?ooooooo`1loooo0`0008Goool000Woool500000_oo o`800007oooo00<0003oooooool0Ooooo`800023oooo000;oooo00D0003oooooooooool000000_oo o`030000oooooooo00Coool00`000?ooooooo`21oooo0`00083oool000_oool01@000?oooooooooo o`000002oooo00<0003oooooool01?ooo`<00024oooo0P0007koool000_oool01@000?oooooooooo o`000002oooo00<0003oooooool01?ooo`030000oooooooo08Koool20000O?ooo`002oooo`050000 oooooooooooo000000;oool00`000?ooooooo`04oooo00<0003oooooool0R?ooo`<0001ioooo000: oooo0P0000Coool200001oooo`030000oooooooo08_oool20000Moooo`006Oooo`030000oooooooo 08goool20000MOooo`006Oooo`030000oooooooo08ooool20000Loooo`006Oooo`030000oooooooo 097oool20000LOooo`006Oooo`030000oooooooo09?oool20000Koooo`006Oooo`030000oooooooo 09Goool30000K?ooo`006Oooo`030000oooooooo09Soool20000J_ooo`006Oooo`030000oooooooo 09[oool20000J?ooo`006Oooo`030000oooooooo09coool20000I_ooo`006Oooo`030000oooooooo 09koool20000I?ooo`006Oooo`030000oooooooo0:3oool30000HOooo`006Oooo`030000oooooooo 0:?oool20000Goooo`006Oooo`030000oooooooo0:Goool20000GOooo`006Oooo`030000oooooooo 0:Ooool20000Foooo`006Oooo`030000oooooooo0:Woool30000F?ooo`006Oooo`030000oooooooo 0:coool30000EOooo`006Oooo`030000oooooooo0:ooool20000Doooo`006Oooo`030000oooooooo 0;7oool30000D?ooo`006Oooo`030000oooooooo0;Coool20000C_ooo`002Oooo`@00003oooo0P00 00Ooool00`000?ooooooo`2foooo0P0004coool000Woool00`000?ooooooo`03oooo00@0003ooooo ool00006oooo0`000;Soool30000BOooo`002_ooo`030000oooooooo00;oool010000?ooooooo`00 00Koool00`000?ooooooo`2koooo0P0004Ooool000_oool01@000?ooooooooooo`000002oooo00<0 003oooooool01?ooo`030000oooooooo0;goool30000A?ooo`002Oooo`040000oooooooo00000_oo o`040000oooooooo00001_ooo`030000oooooooo0<3oool20000@_ooo`002_ooo`800004oooo0P00 00Ooool00`000?ooooooo`32oooo0P00043oool001Woool00`000?ooooooo`34oooo0P0003koool0 01Woool00`000?ooooooo`36oooo0P0003coool001Woool00`000?ooooooo`38oooo0`0003Woool0 01Woool00`000?ooooooo`3;oooo0P0003Ooool001Woool00`000?ooooooo`3=oooo0`0003Coool0 01Woool00`000?ooooooo`3@oooo0`00037oool001Woool00`000?ooooooo`3Coooo0P0002ooool0 01Woool00`000?ooooooo`3Eoooo0P0002goool001Woool00`000?ooooooo`3Goooo0`0002[oool0 01Woool20000foooo`80000Xoooo000Ioooo00<0003oooooool0g?ooo`030000oooooooo02Goool0 01Woool00`000?ooooooo`3Moooo0`0002Coool001Woool00`000?ooooooo`3Poooo0`00027oool0 01Woool00`000?ooooooo`3Soooo0P0001ooool001Woool00`000?ooooooo`3Uoooo00<0003ooooo ool07?ooo`006Oooo`030000oooooooo0>Koool300006oooo`006Oooo`030000oooooooo0>Woool2 00006Oooo`006Oooo`030000oooooooo0>_oool300005_ooo`006Oooo`80003_oooo0P0001Coool0 01Woool00`000?ooooooo`3`oooo0P0001;oool001Woool00`000?ooooooo`3ooooo1Oooo`006Ooo o`030000oooooooo0?ooool5oooo000Ioooo00<0003oooooool0ooooo`Goool001Woool00`000?oo ooooo`3ooooo1Oooo`002_ooo`800004oooo0P0000Ooool00`000?ooooooo`3ooooo1Oooo`002Ooo o`040000oooooooo00000_ooo`040000oooooooo00001_ooo`030000oooooooo0?ooool5oooo000< oooo00@0003oooooool00002oooo00<0003oooooool01?ooo`<0003ooooo1Oooo`002_ooo`800003 oooo00@0003oooooool00006oooo00<0003oooooool0ooooo`Goool000[oool00`000?ooooooo`02 oooo00@0003oooooool00006oooo00<0003oooooool0ooooo`Goool000[oool300000oooo`800007 oooo00<0003oooooool0ooooo`Goool001Woool00`000?ooooooo`3ooooo1Oooo`006Oooo`030000 oooooooo0?ooool5oooo000Ioooo0P000?ooool6oooo000Ioooo00<0003oooooool0ooooo`Goool0 01Woool00`000?ooooooo`3ooooo1Oooo`006Oooo`030000oooooooo0?ooool5oooo000Ioooo00<0 003oooooool0ooooo`Goool001Woool20000ooooo`Koool001Woool00`000?ooooooo`3ooooo1Ooo o`006Oooo`030000oooooooo0?ooool5oooo000Ioooo00<0003oooooool0ooooo`Goool001Woool0 0`000?ooooooo`3ooooo1Oooo`006Oooo`80003ooooo1_ooo`006Oooo`030000oooooooo0?ooool5 oooo000Ioooo00<0003oooooool0ooooo`Goool001Woool00`000?ooooooo`3ooooo1Oooo`006Ooo o`80003ooooo1_ooo`000oooo`D00002oooo0P0000Coool200001oooo`030000oooooooo0?ooool5 oooo0005oooo00D0003oooooooooool000000_ooo`040000oooooooo00000_ooo`030000oooooooo 00Coool00`000?ooooooo`3ooooo1Oooo`001Oooo`050000oooooooooooo000000;oool010000?oo ooooo`0000;oool00`000?ooooooo`04oooo0`000?ooool5oooo0005oooo00D0003oooooooooool0 00000_ooo`040000oooooooo00000_ooo`030000oooooooo0?ooool"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {1.73541, -0.207128, \ 0.00840047, 0.012945}}] }, Open ]], Cell["Momentum transfer cross section relation to diffusion", "Subsection"], Cell[CellGroupData[{ Cell["From Massey and Burhop, p. 367", "Subsubsection"], Cell["\<\ normtheordiff := 3/16*Sqrt[Pi]*vo^7/p12r (*Eq. \ 3.1 (7)*)\ \>", "Input"], Cell["where", "SmallText"], Cell["vo = Sqrt[2*k*temp/mr];", "Input"], Cell["\<\ We used to believe the expression given by Massey and Burhop should be \ reduced by a factor of 2, but now use their relation\ \>", "SmallText"], Cell["\<\ p12 := 2*Integrate[v^5*qd*Exp[-mr*v^2/(2*k*temp)],{v,0,Infinity}, Assumptions->{mr/k/temp>0}] (*Eq.3.1 \ (8)*)\ \>", "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{p12}, p12]\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(16\ k\^3\ qd\ temp\^3\)\/mr\^3\)], "Output"] }, Open ]], Cell["Apparently Mathematica assumed qd was a constant", "SmallText"], Cell[BoxData[ \(\(qd\ := \ 2*Pi*Integrate[ \((1 - cos[theta])\) I[theta, v] sin[theta], {theta, 0, Pi}]\ (* Eq . \ 3.1\ \((6)\)*) \)\)], "Input", Evaluatable->False], Cell["\<\ For a cross sectiion that can be approximated by qd = qdr*(v/vr)^(2*rm), \ where qdr is the cross section at vo.\ \>", "SmallText"], Cell[CellGroupData[{ Cell["\<\ p12r = qdr/vr^(2*rm)*Integrate[v^5*v^(2*rm)*Exp[-v^2/vo^2],{v,0,Infinity}, Assumptions -> {mr/(k*temp)> 0,rm > -2,vo^2 >0}] \ //PowerExpand\ \>", "Input"], Cell[BoxData[ \(2\^\(2 + rm\)\ k\^\(3 + rm\)\ mr\^\(\(-3\) - rm\)\ qdr\ temp\^\(3 + rm\)\ vr\^\(\(-2\)\ rm\)\ Gamma[3 + rm]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(normtheordiffr\ = \ normtheordiff\ \ /. \ mr\ -> m/2\ // PowerExpand\)], "Input"], Cell[BoxData[ \(\(3\ 2\^\(\(-2\) - 2\ rm\)\ k\^\(1\/2 - rm\)\ m\^\(\(-\(1\/2\)\) + rm\)\ \@\[Pi]\ temp\^\(1\/2 - rm\)\ vr\^\(2\ rm\)\)\/\(qdr\ Gamma[3 + rm]\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Block[{r,vo}, normtheordiff0 = normtheordiffr /. {rm -> 0,vo -> Sqrt[4*k*temp/m],mr->m/2} \ // PowerExpand; normtheordiff1 = normtheordiff0 //. temp -> Pi*m/16/k*vbar^2 // PowerExpand ]\ \>", "Input"], Cell[BoxData[ \(\(3\ \[Pi]\ vbar\)\/\(32\ qdr\)\)], "Output"] }, Open ]], Cell["This agrees approximately the classical (1/3)(vbar/qdr).", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(normtheordiff0\)], "Input"], Cell[BoxData[ \(\(3\ \@k\ \@\[Pi]\ \@temp\)\/\(8\ \@m\ qdr\)\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["From Curtis, Hirshfelder and Bird, p. 527", "Subsubsection"], Cell["\<\ theordiffpure := 3/8*Sqrt[Pi*m*k*temp]/Pi/sigma^2/omega11star/n/m (*Eq. \ 8.2-9*);\ \>", "Input"], Cell["where sigma is the diameter of a reference hard sphere,", "SmallText"], Cell["\<\ omega11star := omega11*Sqrt[Pi*m/k/temp]/Pi/sigma^2 (*Eq.8.2-8 for l=1 \ and s=1*);\ \>", "Input"], Cell["\<\ omega11 := Sqrt[k*temp/Pi/m]*Integrate[y^5*omega1*Exp[-y^2],{y,0,Infinity}, Assumptions->{rc>-2}]; \ (*Eq. 8.2-3*)\ \>", "Input"], Cell["where y^2 = m*v^2/4/k/temp and", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(\(omega1\ = \ 2*Pi*Integrate[\((1 - cos[theta])\) I[theta] sin[theta], {theta, 0, Pi}] \ (*Eq . \ 8.2 - 2*) \)\)], "Input", Evaluatable->False], Cell[BoxData[ \(2\ \[Pi]\ \(\[Integral]\_0\%\[Pi]\( I[theta]\ \((1 - cos[theta])\)\ sin[theta]\) \[DifferentialD]theta\)\)], "Output"] }, Open ]], Cell["\<\ In the last equation we used the relation that b db = I[theta] sin[theta] \ dtheta from McDaniel,Mitchell, and Rudd, p. 8, Eq. 3-7-1. We note that \ omega1 = qd from above and from Masey and Burhop, p. 367.\ \>", "SmallText", PageWidth->WindowWidth], Cell[CellGroupData[{ Cell["Evaluation of omega11 without specification of omega1:", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(theordiffpure\ // \ PowerExpand\)], "Input"], Cell[BoxData[ \(\(3\ \@k\ \@\[Pi]\ \@temp\)\/\(8\ \@m\ n\ omega1\)\)], "Output"] }, Open ]], Cell["\<\ Mathematica assumed omega1 was a constant. The result agrees with that \ obtained with the formulas originally given on p. 367 of Massey and Burhop.\ \>", "SmallText"] }, Open ]], Cell["\<\ For a cross sectiion that can be approximated by omega1 = qd = \ qdr*(v/vr)^(2*rc) = qdr*y^(2*rc)*(vo/vr)^(2*rc), where qdr is the cross \ section at vo.\ \>", "SmallText"], Cell[BoxData[ \(\(omega1\ = \ qdr*y^\((2*rc)\)*\((vo/vr)\)^\((2*rc)\)\ ; \)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(omega11\ \ // PowerExpand\)], "Input"], Cell[BoxData[ \(\(2\^\(\(-1\) + rc\)\ k\^\(1\/2 + rc\)\ mr\^\(-rc\)\ qdr\ temp\^\(1\/2 + rc\)\ vr\^\(\(-2\)\ rc\)\ Gamma[3 + rc]\)\/\(\@m\ \@\[Pi]\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(theornormdiffpure\ = \ theordiffpure\ *n\ \ /. \ mr\ -> m/2\ // \ PowerExpand\)], "Input"], Cell[BoxData[ \(\(3\ 2\^\(\(-2\) - 2\ rc\)\ k\^\(1\/2 - rc\)\ m\^\(\(-\(1\/2\)\) + rc\)\ \@\[Pi]\ temp\^\(1\/2 - rc\)\ vr\^\(2\ rc\)\)\/\(qdr\ Gamma[3 + rc]\)\)], "Output"] }, Open ]] }, Open ]], Cell["Determination of empirical diffusion cross section", "Subsection"], Cell[CellGroupData[{ Cell["\<\ empnormdiff = empnormdiff /. temp -> mr*vo^2/2/k //PowerExpand\ \>", "Input"], Cell[BoxData[ RowBox[{"0.092670876502504651`", " ", SuperscriptBox["temp", StyleBox["0.660000000000000053`", StyleBoxAutoDelete->True, PrintPrecision->2]]}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(coefemp\ = \ Coefficient[empnormdiff, temp^r]\)], "Input"], Cell[BoxData[ \(0.092670876502504651`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(theornormdiffpure\)], "Input"], Cell[BoxData[ \(\(3\ 2\^\(\(-2\) - 2\ rc\)\ k\^\(1\/2 - rc\)\ m\^\(\(-\(1\/2\)\) + rc\)\ \@\[Pi]\ temp\^\(1\/2 - rc\)\ vr\^\(2\ rc\)\)\/\(qdr\ Gamma[3 + rc]\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(coeftheor\ = \ Coefficient[theornormdiffpure, temp^\((1/2 - \ \ rc)\)]\)], "Input"], Cell[BoxData[ \(\(3\ 2\^\(\(-2\) - 2\ rc\)\ k\^\(1\/2 - rc\)\ m\^\(\(-\(1\/2\)\) + rc\)\ \@\[Pi]\ vr\^\(2\ rc\)\)\/\(qdr\ Gamma[3 + rc]\)\)], "Output"] }, Open ]], Cell["\<\ In the present case the experimental data is consistent with 0.5 - rc = 0.73 \ or\ \>", "SmallText"], Cell["\<\ rc = 0.5 - r; k = 1.381*10^(-23); mr = 2*1.66*10^(-27); qe = 1.602*10^(-19); m=mr*2; vr = (2*qe*1/mr)^0.5; (*for vr at a relative energy of 1 eV*)\ \>", "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Gamma[2.77]\)], "Input"], Cell[BoxData[ \(1.63506073608500157`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(rc\)], "Input"], Cell[BoxData[ \(\(-0.160000000000000035`\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(coeftheor\)], "Input"], Cell[BoxData[ \(7.8195728730552938`\/qdr\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(vr\)], "Input"], Cell[BoxData[ \(9823.74796584203835`\)], "Output"] }, Open ]], Cell["\<\ Here we converted vo to an equivalent center of mass or relative energy u in \ eV.\ \>", "SmallText"], Cell[CellGroupData[{ Cell["soldiff = Solve[coeftheor == 10^21*coefemp, {qdr}]", "Input"], Cell[BoxData[ \({{qdr \[Rule] 8.43800465494027385`*^-20}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["qd1 = (qdr /. soldiff )*u^rc", "Input"], Cell[BoxData[ \({8.43800465494027385`*^-20\/u\^0.160000000000000035`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["qd1 /. u -> 0.01 (*laboratory energy = 0.02 eV*)", "Input"], Cell[BoxData[ \({1.76294904776950822`*^-19}\)], "Output"] }, Open ]], Cell["Viscosity cross section", "Section"], Cell["\<\ We determine the viscosity cross section the same way as we did the diffusion \ cross section\ \>", "SmallText"], Cell["Input data", "Subsection"], Cell["From viscosity measurements", "Subsubsection"], Cell[CellGroupData[{ Cell["!!a:\\chapman.dat ", "Input"], Cell["\<\ %Viscosity of He 10E7*mu (poise) %from Table 12 , p230 of Chapman and Cowling(1970) -258.1 294.6 -197.6 817.6 -102.6 1392 17.6 1967 183.7 2681 392 3388 815 4703 \ \>", "Print"] }, Open ]], Cell[BoxData[ \(<< Miscellaneous`Units`\)], "Input"], Cell[CellGroupData[{ Cell["Convert[1 Poise, Kilo Gram Meter^-1 Second^-1]", "Input", CellTags->"S5.63.1"], Cell[BoxData[ \(\(0.1`\ Gram\ Kilo\)\/\(Meter\ Second\)\)], "Output"] }, Open ]], Cell[BoxData[ \(Block[{inputfile}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*1\ poise\ = \ 0.1\ \(kgm/m\)/s*) \ninputfile := "\"; \n stream = OpenRead[inputfile]; Find[stream, "\<%\>"]; Find[stream, "\<%\>"]; \n viscinput = ReadList[stream, Number, RecordLists \[Rule] True]; \n Close[stream]; \n]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(viscinput1\ = \ Transpose[{\((\ 273.2 + Part[Transpose[viscinput], 1])\), 0.1*1.*^-7*Part[Transpose[viscinput], 2]}]\ \)\)], "Input"], Cell[BoxData[ \({{15.0999999999999667`, 2.94600000000000061`*^-6}, { 75.599999999999996`, 8.17600000000000193`*^-6}, { 170.599999999999996`, 0.0000139200000000000013`}, { 290.800000000000036`, 0.0000196700000000000052`}, { 456.899999999999995`, 0.0000268100000000000049`}, { 665.200000000000102`, 0.0000338800000000000167`}, { 1088.20000000000028`, 0.0000470300000000000029`}}\)], "Output"] }, Open ]], Cell["\<\ visclistplot = LogLogListPlot[viscinput1, (*AxesLabel -> {\"Viscosity \ (kgm/m/s)\",\"Temperature (K)\"},*) PlotRange -> \ {{100,10000},{1*^-5,1*^-4}}, PlotStyle -> PointSize[0.02], DisplayFunction -> Identity];\ \>", "Input"], Cell["From thermal conductivity (lambda) meaurements", "Subsubsection"], Cell[CellGroupData[{ Cell["!!a:\\saxena.dat ", "Input"], Cell["\<\ %Thermal conductivity of He in mW cm^-1 K^-1 versus T in K %From Table 1, Saxena (1971) 350 1.704 400 1.843 450 1.982 500 2.121 550 2.260 600 2.400 650 2.539 700 2.687 750 2.817 800 2.955 850 3.093 900 3.230 950 3.366 1000 3.501 1050 3.636 1100 3.768 1150 3.900 1200 4.043 1250 4.158 1300 4.285 1350 4.409 1400 4.532 1450 4.653 1500 4.771 \ \>", "Print"] }, Open ]], Cell[BoxData[ \(<< Miscellaneous`Units`\)], "Input"], Cell[CellGroupData[{ Cell["\<\ Convert[1 Milli Watt/(Centi Meter)/Kelvin, Watt/Meter/Kelvin]\ \>", "Input", Evaluatable->False, CellTags->"S5.63.1"], Cell[BoxData[ \(Watt\/\(10\ Kelvin\ Meter\)\)], "Output"] }, Open ]], Cell[BoxData[ \(Block[{inputfile}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*1\ \(mW/cm\)/K\ = \ 0.1\ \(W/m\)/K*) \n inputfile := "\"; \nstream = OpenRead[inputfile]; Find[stream, "\<%\>"]; Find[stream, "\<%\>"]; \n lambdainput = ReadList[stream, Number, RecordLists \[Rule] True]; \n Close[stream]; \n]\)], "Input"], Cell[BoxData[ \(\(lambdainput; \)\)], "Input"], Cell["\<\ We need to convert the thermal conductivity to viscosity using the relation \ lambda = 5/2*mu*cv/m, where cv = 3/2*k or mu = 4/15*m/k *lambda. Here k/m = \ 1.381*^-23/4/1.661*^-27 = 4.16*^3 joule/K/kgm.\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(visclambdainput1\ = \ Transpose[{\((\ Part[Transpose[lambdainput], 1])\), \n \t\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(4/15\)/1.381*^-23*4*1.661*^-27*0.1* Part[Transpose[lambdainput], 2]}]\)], "Input"], Cell[BoxData[ \({{350, 0.0000218612136133236756`}, {400, 0.0000236444933622978492`}, { 450, 0.0000254277731112720184`}, {500, 0.0000272110528602461965`}, { 550, 0.0000289943326092203612`}, {600, 0.0000307904417089065907`}, { 650, 0.0000325737214578807598`}, {700, 0.0000344724653632633248`}, { 750, 0.0000361402809558291071`}, {800, 0.0000379107313540912382`}, { 850, 0.0000396811817523533605`}, {900, 0.0000414388027999034491`}, { 950, 0.0000431835944967414953`}, {1000, 0.0000449155568428674811`}, { 1050, 0.0000466475191889934848`}, {1100, 0.0000483409934829833431`}, { 1150, 0.0000500344677769732015`}, {1200, 0.0000518690649287955451`}, { 1250, 0.0000533444402606806633`}, {1300, 0.0000549737678011102914`}, { 1350, 0.0000565646072894038098`}, {1400, 0.0000581426174269852769`}, { 1450, 0.0000596949688631426411`}, {1500, 0.0000612088322471638779`}} \)], "Output"] }, Open ]], Cell["\<\ conductlistplot = LogLogListPlot[visclambdainput1, PlotRange -> \ {{100,10000},{1*^-5,1*^-4}}, PlotStyle -> PointSize[0.02], DisplayFunction -> Identity];\ \>", "Input"], Cell["\<\ In the following we compromise with the diffusion data and use s = 0.73.\ \>", "SmallText"], Cell[BoxData[ \(\(s = 0.66; \)\)], "Input"], Cell["empvisc = 9.35*^-5*(visctemp/3000)^s; (*kgm.m^-1s^-1*)", "Input"], Cell["\<\ empviscplot = LogLogPlot[empvisc, {visctemp,100,10000}, PlotRange -> \ {{100,10000},{1*^-5,1*^-4}} , DisplayFunction -> Identity];\ \>", "Input"], Cell[CellGroupData[{ Cell["\<\ Show[empviscplot,visclistplot, conductlistplot, AxesLabel -> {\"Temperature(K)\",\"Viscosity(kgm/m/s)\"}, DisplayFunction -> $DisplayFunction];\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -1 0.5 3.09017 0.618034 [ [.15051 -0.0125 -11 -12.875 ] [.15051 -0.0125 11 0 ] [.34949 -0.0125 -11 -12.875 ] [.34949 -0.0125 11 0 ] [.5 -0.0125 -14 -12.875 ] [.5 -0.0125 14 0 ] [.65051 -0.0125 -14 -12.875 ] [.65051 -0.0125 14 0 ] [.84949 -0.0125 -14 -12.875 ] [.84949 -0.0125 14 0 ] [1 -0.0125 -17 -12.875 ] [1 -0.0125 17 0 ] [1.025 0 0 -6.4375 ] [1.025 0 88 6.4375 ] [-0.0125 .10883 -52 -6.4375 ] [-0.0125 .10883 0 6.4375 ] [-0.0125 .18605 -46 -6.4375 ] [-0.0125 .18605 0 6.4375 ] [-0.0125 .29488 -46 -6.4375 ] [-0.0125 .29488 0 6.4375 ] [-0.0125 .43199 -46 -6.4375 ] [-0.0125 .43199 0 6.4375 ] [-0.0125 .5223 -46 -6.4375 ] [-0.0125 .5223 0 6.4375 ] [0 .64303 -56.25 0 ] [0 .64303 56.25 12.875 ] [ -0.0005 -0.0005 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid .15051 0 m .15051 .00625 L s gsave .15051 -0.0125 -72 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (200) show 81.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .34949 0 m .34949 .00625 L s gsave .34949 -0.0125 -72 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (500) show 81.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .5 0 m .5 .00625 L s gsave .5 -0.0125 -75 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (1000) show 87.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .65051 0 m .65051 .00625 L s gsave .65051 -0.0125 -75 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (2000) show 87.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .84949 0 m .84949 .00625 L s gsave .84949 -0.0125 -75 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (5000) show 87.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 1 0 m 1 .00625 L s gsave 1 -0.0125 -78 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (10000) show 93.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .001 w .23856 0 m .23856 .00375 L s .30103 0 m .30103 .00375 L s .38908 0 m .38908 .00375 L s .42255 0 m .42255 .00375 L s .45154 0 m .45154 .00375 L s .47712 0 m .47712 .00375 L s .73856 0 m .73856 .00375 L s .80103 0 m .80103 .00375 L s .88908 0 m .88908 .00375 L s .92255 0 m .92255 .00375 L s .95154 0 m .95154 .00375 L s .97712 0 m .97712 .00375 L s .25 Mabswid 0 0 m 1 0 L s gsave 1.025 0 -61 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (Temperature) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 129.000000 13.000000 moveto (H) show 135.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (K) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 141.000000 13.000000 moveto (L) show 147.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Math2Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math2Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: Math2Mono %%+ Courier grestore 0 .10883 m .00625 .10883 L s gsave -0.0125 .10883 -113 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.000015) show 111.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .18605 m .00625 .18605 L s gsave -0.0125 .18605 -107 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.00002) show 105.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .29488 m .00625 .29488 L s gsave -0.0125 .29488 -107 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.00003) show 105.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .43199 m .00625 .43199 L s gsave -0.0125 .43199 -107 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.00005) show 105.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .5223 m .00625 .5223 L s gsave -0.0125 .5223 -107 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.00007) show 105.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .001 w 0 .02558 m .00375 .02558 L s 0 .04894 m .00375 .04894 L s 0 .07042 m .00375 .07042 L s 0 .09031 m .00375 .09031 L s 0 .12615 m .00375 .12615 L s 0 .14243 m .00375 .14243 L s 0 .15777 m .00375 .15777 L s 0 .17228 m .00375 .17228 L s 0 .37209 m .00375 .37209 L s 0 .48092 m .00375 .48092 L s 0 .55814 m .00375 .55814 L s 0 .58975 m .00375 .58975 L s .25 Mabswid 0 0 m 0 .61803 L s gsave 0 .64303 -117.25 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (Viscosity) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 117.000000 13.000000 moveto (H) show 123.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (kgm) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 141.250000 13.000000 moveto (\\220) show 147.250000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (m) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 153.500000 13.000000 moveto (\\220) show 159.500000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (s) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 165.500000 13.000000 moveto (L) show 171.500000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Math2Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math2Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: Math2Mono %%+ Courier grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .0031 0 m .35018 .28316 L .48647 .39434 L .56532 .45866 L .62109 .50416 L .66799 .54243 L .70522 .57279 L .73884 .60022 L s .73884 .60022 m .76067 .61803 L s .02 w .11599 .08877 Mdot .2318 .18158 Mdot .32991 .2647 Mdot .41148 .32752 Mdot .51835 .41555 Mdot .27203 .20993 Mdot .30103 .23098 Mdot .32661 .25049 Mdot .34949 .26869 Mdot .37018 .28573 Mdot .38908 .30186 Mdot .40646 .31697 Mdot .42255 .33218 Mdot .43753 .34486 Mdot .45154 .35769 Mdot .46471 .36995 Mdot .47712 .38158 Mdot .48886 .39265 Mdot .5 .4032 Mdot .51059 .41336 Mdot .5207 .42293 Mdot .53035 .43217 Mdot .53959 .44184 Mdot .54846 .44937 Mdot .55697 .45744 Mdot .56517 .4651 Mdot .57306 .47248 Mdot .58068 .47956 Mdot .58805 .48628 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooo00@0003oooooool00002 oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`050000oooooooooooo000000;oool0 10000?ooooooo`0000;oool010000?ooooooo`0000;oool200001?ooo`040000oooooooo00000_oo o`040000oooooooo00000_ooo`040000oooooooo00002Oooo`040000oooooooo00000_ooo`040000 oooooooo00000_ooo`050000oooooooo0000oooo00800002oooo00@0003oooooool00002oooo00@0 003oooooool00002oooo00@0003oooooool00002oooo00@0003oooooool0001?oooo0017oooo00D0 003oooooooooool000000_ooo`040000oooooooo00000_ooo`030000oooooooo00[oool200000ooo o`040000oooooooo00000_ooo`040000oooooooo00001?ooo`050000oooooooooooo000000;oool0 10000?ooooooo`0000;oool010000?ooooooo`0000;oool00`000?ooo`000003oooo00@0003ooooo ool00002oooo00@0003oooooool00002oooo00@0003oooooool00007oooo0P0000?oool010000?oo ooooo`0000;oool010000?ooooooo`0000;oool010000?ooo`00000000;oool010000?ooooooo`00 00;oool010000?ooooooo`0000;oool010000?ooooooo`0000;oool010000?ooooooo`0004ooool0 04Goool010000?ooooooo`0000;oool010000?ooooooo`0000;oool010000?ooooooo`0000coool0 0`000?ooooooo`02oooo00@0003oooooool00002oooo00@0003oooooool00004oooo00D0003ooooo ooooool000000_ooo`040000oooooooo00000_ooo`040000oooooooo00000_ooo`040000oooooooo 00000_ooo`040000oooooooo00000_ooo`040000oooooooo00000_ooo`040000oooooooo00001ooo o`030000oooooooo00;oool010000?ooooooo`0000;oool010000?ooooooo`0000;oool010000?oo o`00000000;oool010000?ooooooo`0000;oool010000?ooooooo`0000;oool010000?ooooooo`00 00;oool010000?ooooooo`0004ooool004Koool200001?ooo`800004oooo0P0000goool300000ooo o`800004oooo0P0000Coool200001?ooo`800004oooo0P0000Coool2000000?oool0000000001?oo o`800004oooo0P0000Coool200002?ooo`<00003oooo0P0000Coool200001?ooo`800004oooo0P00 00Coool200001?ooo`800004oooo0P00053oool00?oooolQoooo003Koooo0`00037oool00`000?oo ooooo`06oooo00<0003oooooool01Oooo`00g?ooo`030000oooooooo02ooool00`000?ooooooo`08 oooo00<0003oooooool01?ooo`00b_ooo`<00004oooo0`000008oooo00000000oooo0000oooo0000 oooo0`0000Coool300000_ooo`@00002oooo1@0000;oool200001?ooo`@000000oooo`0000000002 00000oooo`<00003oooo00@0003oooooooooool3000000?oool0000000000oooo`030000oooooooo 00?oool003Sooon<00001oooo`030000oooooooo00;oool00`000?ooooooo`03oooo00L0003oool0 003oool0003oool000000_ooo`040000oooooooo00001_ooo`030000oooooooo00;oool400000_oo o`040000oooooooo00000_ooo`040000oooooooo00000oooo`030000oooooooo00;oool00`000?oo ooooo`04oooo00<0003oooooool00_ooo`040000oooooooo00001?ooo`030000oooooooo00?oool0 03Soool200004oooo`030000oooooooo00Woool00`000?ooooooo`06oooo00<0003oooooool00ooo o`030000oooooooo00?oool00`000?ooooooo`02oooo00D0003oooooooooool000000_ooo`040000 oooooooo00005?ooo`030000oooooooo00[oool00`000?ooooooo`05oooo00<0003oooooool01?oo o`030000oooooooo00?oool01@000?ooooooooooo`000003oooo00D0003oooooooooool000000_oo o`030000oooooooo00Goool00`000?ooooooo`02oooo100000;oool01`000?ooo`000?ooo`000?oo o`000002oooo00<0003oooooool0100000?oool00`000?ooooooo`05oooo00@0003oooooool00005 oooo00@0003oooooool00003oooo00<0003oooooool00_ooo`@00003oooo00<0003oooooool00_oo o`<00005oooo00<0003oooooool00oooo`00>?ooo`040000oooo00000000Soooo`030000oooooooo 00?oool200000_ooo`<000000oooo`000?ooo`0400001?ooo`800003oooo100000?oool3000000?o ool0000000000`000004oooo00000000oooo0P0000;oool400000oooo`800004oooo00<0003ooooo ool00_ooo`030000oooo000000Goool00`000?ooooooo`03oooo000hoooo00D0003oooooooooool0 0000S?ooo`050000oooo0000oooo000002Koool00`000?ooooooo`0Goooo00D0003oooooooooool0 00000_ooo`050000oooooooooooo000000Koool003Soool00`000?ooooooo`02oooo00<0003ooooo ool0ROooo`D00011oooo00<0003oool000000P000005oooo00000000oooo000000Ooool003Soool0 0`000?ooooooo`03oooo00<0003oooooool0goooo`00>?ooo`030000oooooooo00Coool00`000?oo ooooo`3Noooo000hoooo00<0003oooooool01Oooo`80003Noooo000hoooo00<0003oooooool01ooo o`030000oooooooo0=_oool003Soool00`000?ooooooo`08oooo00<0003oooooool0f_ooo`00>?oo o`030000oooooooo00Woool00`000?ooooooo`3Ioooo000hoooo00<0003oooooool02_ooo`80003I oooo000hoooo00<0003oooooool03?ooo`80003Goooo000hoooo00<0003oooooool03?ooo`80003G oooo0006oooo0P0000Coool200001?ooo`800004oooo0P0000Coool200001?ooo`800003oooo1@00 00;oool200001_ooo`030000oooooooo00koool00`000?ooooooo`3Doooo0005oooo00@0003ooooo ool00008oooo00@0003oooooool00002oooo00@0003oooooool00002oooo00@0003oooooool00002 oooo00@0003oooooool00004oooo00D0003oooooooooool000000_ooo`030000oooooooo00?oool2 00004?ooo`030000oooooooo0=?oool000Goool010000?ooooooo`0000Soool010000?ooooooo`00 00;oool010000?ooooooo`0000;oool010000?ooooooo`0000;oool010000?ooooooo`0000Coool0 0`000?ooooooo`04oooo00<0003oooooool00oooo`030000oooooooo013oool20000doooo`001Ooo o`040000oooooooo00002?ooo`040000oooooooo00000_ooo`040000oooooooo00000_ooo`040000 oooooooo00000_ooo`040000oooooooo00001?ooo`030000oooooooo00;oool200001_ooo`030000 oooooooo01;oool00`000?ooooooo`3@oooo0005oooo00@0003oooooool00008oooo00@0003ooooo ool00002oooo00@0003oooooool00002oooo00@0003oooooool00002oooo00@0003oooooool00004 oooo00<0003oooooool00_ooo`030000oooooooo00Goool00`000?ooooooo`0Coooo00<0003ooooo ool0coooo`001_ooo`80000:oooo0P0000Coool200001?ooo`800004oooo0P0000Coool200001?oo o`<00005oooo00<0003oooooool05?ooo`030000oooooooo0?ooo`030000 oooooooo01Soool00`000?ooooooo`3:oooo000hoooo00<0003oooooool06Oooo`030000oooooooo 0?ooo`<0002Z oooo000hoooo00<0003oooooool0>Oooo`80002Zoooo000hoooo00<0003oooooool0>oooo`80002X oooo000hoooo00<0003oooooool0>oooo`80002Xoooo000hoooo00<0003oooooool0?Oooo`80002V oooo000hoooo00<0003oooooool0?Oooo`<0002Uoooo000hoooo00<0003oooooool0?_ooo`<0002T oooo000hoooo00<0003oooooool0@?ooo`80002Soooo000hoooo00<0003oooooool0@?ooo`@0002Q oooo000hoooo00<0003oooooool0@_ooo`80002Qoooo000hoooo00<0003oooooool0@oooo`<0002O oooo000?ooo`030000oooooooo04Woool5 0000Uoooo`00>?ooo`030000oooooooo04_oool40000U_ooo`00>?ooo`030000oooooooo04coool4 0000UOooo`00>?ooo`030000oooooooo04goool50000Toooo`00>?ooo`030000oooooooo04koool2 00000_ooo`030000oooooooo093oool003Soool00`000?ooooooo`1Coooo00<0003oooooool0Sooo o`003?ooo`800004oooo0P0000Coool200001?ooo`800004oooo0P0000Coool200001Oooo`030000 oooooooo00Coool00`000?ooooooo`1Doooo00<0003oooooool0S_ooo`002oooo`040000oooooooo 00002?ooo`040000oooooooo00000_ooo`040000oooooooo00000_ooo`040000oooooooo00000_oo o`040000oooooooo00001?ooo`030000oooooooo00Coool00`000?ooooooo`1Eoooo00<0003ooooo ool0SOooo`002oooo`040000oooooooo00002?ooo`040000oooooooo00000_ooo`040000oooooooo 00000_ooo`040000oooooooo00000_ooo`040000oooooooo00001?ooo`030000oooooooo00Coool2 0000Eoooo`80002=oooo000;oooo00@0003oooooool00008oooo00@0003oooooool00002oooo00@0 003oooooool00002oooo00@0003oooooool00002oooo00@0003oooooool00005oooo00<0003ooooo ool00oooo`030000oooooooo05Soool00`000?ooooooo`2:oooo000;oooo00@0003oooooool00008 oooo00@0003oooooool00002oooo00@0003oooooool00002oooo00@0003oooooool00002oooo00@0 003oooooool00002oooo00@0003oooooool00005oooo00<0003oooooool0FOooo`030000oooooooo 08Woool000coool200002_ooo`800004oooo0P0000Coool200001?ooo`800003oooo100000Goool0 0`000?ooooooo`1Joooo00<0003oooooool0R?ooo`00>?ooo`030000oooooooo05_oool00`000?oo ooooo`27oooo000hoooo00<0003oooooool0G?ooo`800027oooo000hoooo00<0003oooooool0G_oo o`030000oooooooo08Coool003Soool00`000?ooooooo`1Ooooo00<0003oooooool0Poooo`00>?oo o`030000oooooooo063oool00`000?ooooooo`22oooo000hoooo00<0003oooooool0HOooo`800022 oooo000hoooo00<0003oooooool0Hoooo`030000oooooooo07ooool003Soool00`000?ooooooo`1T oooo00<0003oooooool0O_ooo`00>?ooo`030000oooooooo06Goool20000O_ooo`00>?ooo`030000 oooooooo06Ooool00`000?ooooooo`1koooo003ooooo8Oooo`00ooooob7oool00?oooolQoooo003o oooo8Oooo`00ooooob7oool00?oooolQoooo000coooo0P0000Ooool00`000?ooooooo`06oooo0`00 027oool00`000?ooooooo`2doooo000doooo00<0003oooooool01?ooo`030000oooooooo00[oool0 0`000?ooooooo`06oooo00<0003oooooool02Oooo`030000oooooooo00[oool00`000?ooooooo`2c oooo0004oooo0P0000Coool300000_ooo`<00004oooo0`0000?oool200000oooo`<00004oooo0`00 00?oool200001Oooo`030000oooooooo00;oool010000?ooooooooooo`8000000oooo`0000000003 oooo0`000007oooo00000000oooo0000oooo000000;oool010000?ooooooooooo`8000001?ooo`00 0?ooo`0000;oool00`000?ooooooo`02oooo0`0000Goool00`000?ooooooo`2boooo0003oooo00@0 003oooooool00004oooo00<0003oooooool01?ooo`040000oooooooo00001Oooo`040000oooooooo 00001Oooo`030000oooooooo00;oool01@000?ooooooooooo`000002oooo00L0003oooooooooool0 003oool000000oooo`030000oooooooo00;oool00`000?ooo`000003oooo00@0003oooooool00002 oooo00D0003oool0003oool000000_ooo`030000oooooooo00;oool01@000?ooo`000?ooo`000002 oooo00<0003oooooool01Oooo`030000oooooooo00;oool00`000?ooooooo`2boooo0003oooo00@0 003oooooool00004oooo00@0003oooooooooool300000oooo`030000oooooooo00?oool010000?oo ooooo`0000;oool300001Oooo`050000oooooooooooo000000Goool010000?ooooooo`0000?oool0 0`000?ooooooo`02oooo0`0000?oool010000?ooooooo`0000;oool01@000?ooo`000?ooo`000002 oooo00<0003oooooool00_ooo`050000oooo0000oooo000000;oool00`000?ooooooo`02oooo0`00 00Goool00`000?ooooooo`2boooo0003oooo00@0003oooooool00003oooo0P0000?oool400000ooo o`<00003oooo0P0000?oool400000oooo`800002oooo1@000005oooo000000000000oooo00800002 oooo00<0003oooooool00_ooo`040000oooo000000000oooo`L000000oooo`000?ooo`03oooo00<0 003oooooool00`000003oooo0000oooo00?oool010000?ooooooooooo`@00004oooo00<0003ooooo ool0/_ooo`000_ooo`030000oooooooo00;oool00`000?ooooooo`0Soooo00<0003oooooool02ooo o`050000oooooooooooo000001?oool00`000?ooooooo`09oooo00<0003oooooool02?ooo`030000 oooooooo0;?oool000;oool200000_ooo`800003oooo00<0003oooooool06oooo`030000oooooooo 013oool010000?ooo`00000001Coool00`000?ooooooo`09oooo00<0003oooooool01_ooo`030000 oooooooo0;Coool00?oooolQoooo003ooooo8Oooo`00ooooob7oool00?oooolQoooo003ooooo8Ooo o`00ooooob7oool00?oooolQoooo003ooooo8Oooo`00ooooob7oool00?oooolQoooo003ooooo8Ooo o`00ooooob7oool00?oooolQoooo003ooooo8Oooo`00ooooob7oool00?oooolQoooo003ooooo8Ooo o`00ooooob7oool00?oooolQoooo003ooooo8Oooo`00ooooob7oool00?oooolQoooo003ooooo8Ooo o`00ooooob7oool00?oooolQoooo003ooooo8Oooo`00ooooob7oool00?oooolQoooo003ooooo8Ooo o`00ooooob7oool00?oooolQoooo003ooooo8Oooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {1.19219, -5.51774, \ 0.0143609, 0.0116182}}] }, Open ]], Cell["\<\ This plot suggests a more rapid variation of the viscosity at higher \ temperatures.\ \>", "Subsubtitle"], Cell["ClearAll[k,mr,vo,s,vr,m,qe]", "Input"], Cell["Viscosity cross section relation to viscosity coefficient", "Subsection"], Cell[CellGroupData[{ Cell["From Massey and Burhop, p. 368", "Subsubsection"], Cell["\<\ theorvisc := 10*k^3*visctemp^3/m^2*Sqrt[4*Pi*k*visctemp/m]^3/Pi/r11 // \ PowerExpand (*Eq. 3.1 (10)*)\ \>", "Input"], Cell["In general", "SmallText"], Cell["\<\ r11 := 1/2*Integrate[v^7*qv*Exp[-m*v^2/(4*k*visctemp)],{v,0,Infinity}, Assumptions ->{m/k/visctemp>0}] \ (*Eq. 3.1 (11)*)\ \>", "Input", Evaluatable->False], Cell["where", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(\(qv = \ 2*Pi*Integrate[I[theta] \((sin[theta])\)^3, {theta, 0, Pi}] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*Eq . \ 3.1\ \((11)\)*) \)\)], "Input", Evaluatable->False], Cell[CellGroupData[{ Cell["Block[{theorvisc}, N[theorvisc // PowerExpand] ]", "Input"], Cell[BoxData[ \(\(80\ k\^\(9/2\)\ \@\[Pi]\ visctemp\^\(9/2\)\)\/\(m\^\(7/2\)\ r11\)\)], "Output"] }, Open ]], Cell["Here Mathematica assumed qv was a constant.", "SmallText"] }, Open ]], Cell["\<\ For a cross section that can be approximated by qvs*(v/vr)^(2*sm), where qvs \ is the viscosity cross section at vr.\ \>", "SmallText"], Cell["\<\ r11s := qvs/2/vr^(2*sm)*Integrate[v^7*v^(2*sm)*Exp[-m*v^2/(4*k*visctemp)],{v,\ 0,Infinity}, Assumptions->{sm>-2,m/k/visctemp>0}] // PowerExpand\ \>", "Input"], Cell[CellGroupData[{ Cell["theorviscs = theorvisc //. r11->r11s ", "Input"], Cell[BoxData[ \(\(5\ 2\^\(\(-2\) - 2\ sm\)\ k\^\(1\/2 - sm\)\ m\^\(1\/2 + sm\)\ \@\[Pi]\ visctemp\^\(1\/2 - sm\)\ vr\^\(2\ sm\)\)\/\(qvs\ Gamma[4 + sm]\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["theorvisc0 = theorviscs /. sm -> 1", "Input"], Cell[BoxData[ \(\(5\ m\^\(3/2\)\ \@\[Pi]\ vr\^2\)\/\(384\ \@k\ qvs\ \@visctemp\)\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["From Curtis, Hirshfelder and Bird, p. 527", "Subsubsection"], Cell["\<\ theorviscpure := 5/16*Sqrt[Pi*m*k*visctempc]/(Pi*sigma^2*omega22star) (*Eq. \ 8.2-10*);\ \>", "Input"], Cell["\<\ where sigma is the radius of a reference hard sphere. Using mr = m/2\ \>", "SmallText"], Cell["\<\ omega22star := omega22*Sqrt[2*Pi*mr/(k*visctempc)]/(Pi*sigma^2*3*(1-(1/3))) \ ;(*Eq.8.2-8 for l=2 and s=2*)\ \>", "Input"], Cell["\<\ omega22 := \ Sqrt[k*visctempc/(2*Pi*mr)]*Integrate[y^7*omega2*Exp[-y^2],{y,0,Infinity}]; (*Eq. 8.2-3*)\ \>", "Input"], Cell["and", "SmallText"], Cell[BoxData[ \(\(omega2\ = \ 2*Pi*Integrate[\((1 - \((cos[theta])\)^2)\) I[theta] sin[theta], \n \t\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ { theta, 0, Infinity}] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*Eq . \ 8.2 - 2*) \)\)], "Input", Evaluatable->False], Cell["\<\ In the last equation we used the relation that b db = I[theta] sin[theta] \ dtheta from McDaniel,Mitchell, and Rudd, p. 8, Eq. 3-7-1. We note that omega2 = qv from above and from Masey and Burhop, p. 368.\ \>", "SmallText"], Cell["\<\ For a cross sectiion that can be approximated by qv = qvs*(v/vr)^(2*sc) = \ qvs*y^(2*sc)*(vos/vr)^(2*sc), where qvs is the viscosity cross section at vr.\ \ \>", "SmallText"], Cell[BoxData[ \(omega2\ = \ qvs*\((y*vos/vr)\)^\((2*sc)\); vos\ = \ Sqrt[2*k*visctempc/mr]; mr = m/2; \)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(theorviscpuresc\ = \ N[theorviscpure\ // \ PowerExpand]\)], "Input"], Cell[BoxData[ \(\(8.86226925452758074`\ 2.`\^\(\(-2.`\) - 2.`\ sc\)\ k\^\(\(0.5`\[InvisibleSpace]\) - 1.`\ sc\)\ m\^\(\(0.5`\[InvisibleSpace]\) + sc\)\ visctempc\^\(\(0.5`\[InvisibleSpace]\) - 1.`\ sc\)\ vr\^\(2.`\ sc\)\)\/\(qvs\ Gamma[\(4.`\[InvisibleSpace]\) + sc]\)\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(theorviscpure1\ = \ theorviscpuresc\ /. \ sc\ -> \ 1\)], "Input"], Cell[BoxData[ \(\(0.0230788261836655728`\ m\^1.5`\ vr\^2.`\)\/\(k\^0.5`\ qvs\ visctempc\^0.5`\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(solqvs\ = \ Solve[theorviscpuresc\ == \ exptvisc, {qvs}]\)], "Input"], Cell[BoxData[ \({{qvs \[Rule] \(2.21556731363189518`\ 2.`\^\(\(-2\)\ sc\)\ k\^\(1\/2 - sc\)\ m\^\(1\/2 + sc\)\ visctempc\^\(1\/2 - sc\)\ vr\^\(2\ sc\)\)\/\(exptvisc\ Gamma[4 + sc]\)}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(qvsc1\ = \ \((\((qvs\ \ /. solqvs)\)\ /. \ vr\ -> \ Sqrt[2*qe*1/mr])\)*\ u^sc\ // \ PowerExpand\)], "Input"], Cell[BoxData[ \({\(2.21556731363189518`\ 1.`\^\(2\ sc\)\ k\^\(1\/2 - sc\)\ \@m\ qe\^sc\ u\^sc\ visctempc\^\(1\/2 - sc\)\)\/\(exptvisc\ Gamma[4 + sc]\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(qvsc1\ /. \ sc\ -> 0\)], "Input"], Cell[BoxData[ \({\(0.369261218938649227`\ \@k\ \@m\ \@visctempc\)\/exptvisc}\)], "Output"] }, Open ]], Cell["From Bird (1981), p. 250", "Subsubsection"], Cell["\<\ For a cross sectiion that can be approximated by qv = qvr*(c/cr)^(2*b) , \ where qdr is the cross section at cr.\ \>", "SmallText"], Cell[CellGroupData[{ Cell["\<\ viscbird = \ 5/8*Sqrt[Pi*m*k*temp]*(m/(4*k*temp))^-4/Integrate[c^7*qvr*(c/cr)^(2*b)*Exp[-m*\ c^2/(4*k*temp)], {c, 0, Infinity}, Assumptions -> m/k/temp > 0] // PowerExpand\ \>", "Input"], Cell[BoxData[ \(\(5\ 2\^\(\(-2\) - 2\ b\)\ cr\^\(2\ b\)\ k\^\(1\/2 - b\)\ m\^\(1\/2 + b\)\ \@\[Pi]\ temp\^\(1\/2 - b\)\)\/\(qvr\ Gamma[4 + b]\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(viscbird1\ = \ viscbird\ /. \ b\ -> \ 0\)], "Input"], Cell[BoxData[ \(\(5\ \@k\ \@m\ \@\[Pi]\ \@temp\)\/\(24\ qvr\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(viscbirdb\ = \ viscbird\ /. \ cr\ -> \ Sqrt[2*qe*ur/\((m/2)\)]\ // \ PowerExpand \)], "Input"], Cell[BoxData[ \(\(5\ k\^\(1\/2 - b\)\ \@m\ \@\[Pi]\ qe\^b\ temp\^\(1\/2 - b\)\ ur\^b\)\/\(4\ qvr\ Gamma[4 + b]\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[viscbirdb\ == \ viscexpt, qvr]\)], "Input"], Cell[BoxData[ \({{qvr \[Rule] \(5\ k\^\(1\/2 - b\)\ \@m\ \@\[Pi]\ qe\^b\ temp\^\(1\/2 - b\)\ ur\^b\)\/\(4\ viscexpt\ Gamma[4 + b]\)}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(qvr1\ = \ viscbirdb*qvr/viscexpt\)], "Input"], Cell[BoxData[ \(\(5\ k\^\(1\/2 - b\)\ \@m\ \@\[Pi]\ qe\^b\ temp\^\(1\/2 - b\)\ ur\^b\)\/\(4\ viscexpt\ Gamma[4 + b]\)\)], "Output"] }, Open ]], Cell["Determination of empirical viscosity cross section", "Subsection"], Cell[CellGroupData[{ Cell["empvisc1 = empvisc //PowerExpand", "Input"], Cell[BoxData[ RowBox[{"4.74145445004068655`*^-7", " ", SuperscriptBox["visctemp", StyleBox["0.660000000000000053`", StyleBoxAutoDelete->True, PrintPrecision->2]]}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(coefempv\ = \ Coefficient[empvisc1, visctemp^0.66]\)], "Input"], Cell[BoxData[ \(4.74145445004068655`*^-7\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(theorviscpuresc\ \)\)], "Input"], Cell[BoxData[ \(\(8.86226925452758074`\ 2.`\^\(\(-2.`\) - 2.`\ sc\)\ k\^\(\(0.5`\[InvisibleSpace]\) - 1.`\ sc\)\ m\^\(\(0.5`\[InvisibleSpace]\) + sc\)\ visctempc\^\(\(0.5`\[InvisibleSpace]\) - 1.`\ sc\)\ vr\^\(2.`\ sc\)\)\/\(qvs\ Gamma[\(4.`\[InvisibleSpace]\) + sc]\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(coeftheor\ = \ Coefficient[viscbirdb, temp^\((1/2 - b)\)]\)], "Input"], Cell[BoxData[ \(\(5\ k\^\(1\/2 - b\)\ \@m\ \@\[Pi]\ qe\^b\ ur\^b\)\/\(4\ qvr\ Gamma[4 + b]\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(coeftheorc\ = \ Coefficient[theorviscpuresc, visctempc^\((0.5 - 1. \ sc)\)]\)], "Input"], Cell[BoxData[ \(\(2.21556731363189518`\ 2.`\^\(\(-2.`\)\ sc\)\ k\^\(\(0.5`\[InvisibleSpace]\) - 1.`\ sc\)\ m\^\(\(0.5`\[InvisibleSpace]\) + sc\)\ vr\^\(2.`\ sc\)\)\/\(qvs\ Gamma[\(4.`\[InvisibleSpace]\) + sc]\)\)], "Output"] }, Open ]], Cell["\<\ In the present case the experimental data is consistent with 0.5 - sc = 0.66 \ or\ \>", "SmallText"], Cell["\<\ s = 0.66; sc = 0.5 - s; b = sc; k = 1.381*10^(-23); mr = 2*1.66*10^(-27); qe = 1.602*10^(-19); m=mr*2; vr = (2*qe*1/mr)^0.5; (*for vr at a relative energy of 1 eV*) ur = 1;\ \>", "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(coeftheor\)], "Input"], Cell[BoxData[ \(3.04706360781027862`*^-26\/qvr\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["solviscb = Solve[coeftheor == coefempv, {qvr}]", "Input"], Cell[BoxData[ \({{qvr \[Rule] 6.42643231083687993`*^-20}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["qv1 = (qvr /. solviscb )*u^b", "Input"], Cell[BoxData[ \({6.42643231083687993`*^-20\/u\^0.160000000000000035`}\)], "Output"] }, Open ]], Cell["\<\ Next we convert to an equivalent center of mass or relative energy u in eV.\ \>", "SmallText"], Cell[CellGroupData[{ Cell["qv1 /. u -> 0.01 (*laboratory energy = 0.02 eV*)", "Input"], Cell[BoxData[ \({1.34267201622268794`*^-19}\)], "Output"] }, Open ]], Cell["An alternate procedure is:", "SmallText"], Cell[CellGroupData[{ Cell["solvisc = Solve[coeftheorc == coefempv, {qvs}]", "Input"], Cell[BoxData[ \({{qvs \[Rule] 6.42643231083688526`*^-20}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["qv1 = (qvs /. solvisc )*u^sc", "Input"], Cell[BoxData[ \({6.42643231083688526`*^-20\/u\^0.160000000000000035`}\)], "Output"] }, Open ]], Cell["\<\ Next we convert to an equivalent center of mass or relative energy u in eV.\ \>", "SmallText"], Cell[CellGroupData[{ Cell["qv1 /. u -> 0.01 (*laboratory energy = 0.02 eV*)", "Input"], Cell[BoxData[ \({1.34267201622268794`*^-19}\)], "Output"] }, Open ]], Cell["Comparison of viscosity and diffusion results", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(crossratio\ = \ qv1/qd1\)], "Input"], Cell[BoxData[ \({0.76160568447593171`}\)], "Output"] }, Open ]], Cell["\<\ The viscosity cross sections are 80% of the diffusion cross sections, \ compared to the ratio of about 2/3 expected for an enegy independent cross \ section. See Hirshfelder, Curtis, and Bird, p. 526.\ \>", "SmallText"], Cell["\<\ We should check to see whether the viscosity and diffusion coefficients have \ the expected relationship from Chapman and Cowling, Eq. (14.5,1), i.e., \ normtheordiff*m/theorvisc = 6/5;\ \>", "SmallText"], Cell["We find from our empirical fits", "SmallText"], Cell[CellGroupData[{ Cell["\<\ Block[{mr}, mr = 2*1.66*10^(-27); expratio = 10^21*empnormdiff/empvisc*(2*mr) /. temp -> visctemp ]\ \>", "Input"], Cell[BoxData[ \(1.29777608634698736`\)], "Output"] }, Open ]], Cell["\<\ This value is somewhat higher than the value of 1.33 given on p. 267 by \ Chapman and Cowling. Unfortunately, Dymond does not discuss this ratio.\ \>", "SmallText"], Cell["\<\ From the Massey and Burhop formulas with the power law temperature dependence\ \ \>", "SmallText"], Cell[CellGroupData[{ Cell["\<\ Block[{mr,vo,qvs,qdr}, mr = m/2; qvs = 2*qdr/3; sm = rm; temp = visctemp; tranratio= m*normtheordiffr/theorviscs // PowerExpand ]\ \>", "Input"], Cell[BoxData[ \(\(2.65599999999999969`*^-27\ 6.63999999999999879`*^-27\^\(\(-\(1\/2\)\) - rm\)\ 1.50602409638554242`*^26\^\(1\/2 - rm\)\ Gamma[4 + rm]\)\/Gamma[ 3 + rm]\)], "Output"], Cell[CellGroupData[{ Cell[BoxData[ \(tranratio\ //. \ rm -> 0\)], "Input"], Cell[BoxData[ \(1.20000000000000017`\)], "Output"] }, Open ]], Cell["This gives the expected theoretical value of 1.2.", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(tranratio\ //. \ rm\ -> 0.5\)], "Input"], Cell[BoxData[ \(1.39999999999999991`\)], "Output"] }, Open ]], Cell["\<\ This is to be compared with the expected theoretical value of 1.55 for \ Maxwellian molecules. See Chapman and Cowling p. 265.\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(tranratio\ //. \ rm\ -> 1\)], "Input"], Cell[BoxData[ \(1.60000000000000008`\)], "Output"] }, Open ]] }, Open ]], Cell["\<\ qd1plot = LogLogPlot[1*^20*Part[qd1,1], {u,0.01,1000}, \ PlotStyle -> {{Dashing[{0.03,0.03}],Thickness[.01]}}, (* PlotStyle -> Hue[0.55],*) PlotRange -> {{0.01,1000}, {0.1,100}}, DisplayFunction -> Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ qv1plot = LogLogPlot[1*^20*Part[qv1,1], {u,0.01,1000}, \ (*PlotStyle -> Dashing[{0.03,0.03}],*) PlotStyle -> {{Hue[0.55],Thickness[.01]}}, PlotRange -> {{0.01,1000}, {0.1,100}}, DisplayFunction -> Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[CellGroupData[{ Cell["\<\ Show[qd1plot,qv1plot, DisplayFunction -> $DisplayFunction, GridLines -> Automatic, AxesLabel -> {\"rel. energy (eV)\",\"q (10^-20 m^2)\"}];\ \>", "Input", PageWidth->Infinity, FontFamily->"Times New Roman", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.4 0.2 0.206011 0.206011 [ [.2 -0.0125 -11 -12.875 ] [.2 -0.0125 11 0 ] [.4 -0.0125 -5 -12.875 ] [.4 -0.0125 5 0 ] [.6 -0.0125 -8 -12.875 ] [.6 -0.0125 8 0 ] [.8 -0.0125 -11 -12.875 ] [.8 -0.0125 11 0 ] [1 -0.0125 -14 -12.875 ] [1 -0.0125 14 0 ] [1.025 0 0 -6.4375 ] [1.025 0 100.25 6.4375 ] [-0.0125 .144 -22 -6.4375 ] [-0.0125 .144 0 6.4375 ] [-0.0125 .20601 -10 -6.4375 ] [-0.0125 .20601 0 6.4375 ] [-0.0125 .35001 -10 -6.4375 ] [-0.0125 .35001 0 6.4375 ] [-0.0125 .41202 -16 -6.4375 ] [-0.0125 .41202 0 6.4375 ] [-0.0125 .55602 -16 -6.4375 ] [-0.0125 .55602 0 6.4375 ] [-0.0125 .61803 -22 -6.4375 ] [-0.0125 .61803 0 6.4375 ] [0 .64303 -44.125 0 ] [0 .64303 44.125 12.875 ] [ -0.0005 -0.0005 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 .5 r .25 Mabswid .2 0 m .2 .61803 L s .4 0 m .4 .61803 L s .6 0 m .6 .61803 L s .8 0 m .8 .61803 L s 1 0 m 1 .61803 L s 0 .10301 m 1 .10301 L s 0 .20601 m 1 .20601 L s 0 .30902 m 1 .30902 L s 0 .41202 m 1 .41202 L s 0 .51503 m 1 .51503 L s 0 .61803 m 1 .61803 L s 0 g .2 0 m .2 .00625 L s gsave .2 -0.0125 -72 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.1) show 81.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .4 0 m .4 .00625 L s gsave .4 -0.0125 -66 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (1) show 69.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .6 0 m .6 .00625 L s gsave .6 -0.0125 -69 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (10) show 75.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .8 0 m .8 .00625 L s gsave .8 -0.0125 -72 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (100) show 81.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 1 0 m 1 .00625 L s gsave 1 -0.0125 -75 -16.875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (1000) show 87.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .001 w .06021 0 m .06021 .00375 L s .09542 0 m .09542 .00375 L s .12041 0 m .12041 .00375 L s .13979 0 m .13979 .00375 L s .15563 0 m .15563 .00375 L s .16902 0 m .16902 .00375 L s .18062 0 m .18062 .00375 L s .19085 0 m .19085 .00375 L s .26021 0 m .26021 .00375 L s .29542 0 m .29542 .00375 L s .32041 0 m .32041 .00375 L s .33979 0 m .33979 .00375 L s .35563 0 m .35563 .00375 L s .36902 0 m .36902 .00375 L s .38062 0 m .38062 .00375 L s .39085 0 m .39085 .00375 L s .46021 0 m .46021 .00375 L s .49542 0 m .49542 .00375 L s .52041 0 m .52041 .00375 L s .53979 0 m .53979 .00375 L s .55563 0 m .55563 .00375 L s .56902 0 m .56902 .00375 L s .58062 0 m .58062 .00375 L s .59085 0 m .59085 .00375 L s .66021 0 m .66021 .00375 L s .69542 0 m .69542 .00375 L s .72041 0 m .72041 .00375 L s .73979 0 m .73979 .00375 L s .75563 0 m .75563 .00375 L s .76902 0 m .76902 .00375 L s .78062 0 m .78062 .00375 L s .79085 0 m .79085 .00375 L s .86021 0 m .86021 .00375 L s .89542 0 m .89542 .00375 L s .92041 0 m .92041 .00375 L s .93979 0 m .93979 .00375 L s .95563 0 m .95563 .00375 L s .96902 0 m .96902 .00375 L s .98062 0 m .98062 .00375 L s .99085 0 m .99085 .00375 L s .25 Mabswid 0 0 m 1 0 L s gsave 1.025 0 -61 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (rel) show 81.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (.) show 93.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (energy) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 135.000000 13.000000 moveto (H) show 141.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (eV) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 153.250000 13.000000 moveto (L) show 159.250000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Math2Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math2Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: Math2Mono %%+ Courier grestore 0 .144 m .00625 .144 L s gsave -0.0125 .144 -83 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.5) show 81.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .20601 m .00625 .20601 L s gsave -0.0125 .20601 -71 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (1) show 69.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .35001 m .00625 .35001 L s gsave -0.0125 .35001 -71 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (5) show 69.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .41202 m .00625 .41202 L s gsave -0.0125 .41202 -77 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (10) show 75.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .55602 m .00625 .55602 L s gsave -0.0125 .55602 -77 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (50) show 75.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore 0 .61803 m .00625 .61803 L s gsave -0.0125 .61803 -83 -10.4375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (100) show 81.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier grestore .001 w 0 .06202 m .00375 .06202 L s 0 .09829 m .00375 .09829 L s 0 .12403 m .00375 .12403 L s 0 .16031 m .00375 .16031 L s 0 .1741 m .00375 .1741 L s 0 .18605 m .00375 .18605 L s 0 .19658 m .00375 .19658 L s 0 .26803 m .00375 .26803 L s 0 .3043 m .00375 .3043 L s 0 .33004 m .00375 .33004 L s 0 .36632 m .00375 .36632 L s 0 .38011 m .00375 .38011 L s 0 .39206 m .00375 .39206 L s 0 .4026 m .00375 .4026 L s 0 .47404 m .00375 .47404 L s 0 .51032 m .00375 .51032 L s 0 .53605 m .00375 .53605 L s 0 .57233 m .00375 .57233 L s 0 .58612 m .00375 .58612 L s 0 .59807 m .00375 .59807 L s 0 .60861 m .00375 .60861 L s .25 Mabswid 0 0 m 0 .61803 L s gsave 0 .64303 -105.125 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.875 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.875000 moveto 460.000000 16.875000 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.875000 lineto closepath clip newpath 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (q) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 75.000000 13.000000 moveto (H) show 81.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (10) show 93.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (^) show 99.000000 13.000000 moveto %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (-) show 105.000000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (20) show 123.000000 13.000000 moveto (m) show 129.250000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (^) show 135.250000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (2) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 141.250000 13.000000 moveto (L) show 147.250000 13.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Math1Mono %%+ font Math2Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math1Mono %%+ Math2Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: Math1Mono %%+ Math2Mono %%+ Courier grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .01 w [ .03 .03 ] 0 setdash .00036 .46269 m .72166 .34382 L .7857 .33326 L .82033 .32755 L .84419 .32362 L .86397 .32036 L .87952 .3178 L .89347 .3155 L .90507 .31359 L .91494 .31196 L .92434 .31041 L .93252 .30906 L .93971 .30788 L .94677 .30671 L .95307 .30568 L .95929 .30465 L .96489 .30373 L .96996 .30289 L .97505 .30205 L .97968 .30129 L .98434 .30052 L .98861 .29982 L .99253 .29917 L .99651 .29852 L 1 .29794 L s 0 .7 1 r [ ] 0 setdash .00036 .43833 m .72166 .31945 L .7857 .3089 L .82033 .30319 L .84419 .29926 L .86397 .296 L .87952 .29343 L .89347 .29113 L .90507 .28922 L .91494 .2876 L .92434 .28605 L .93252 .2847 L .93971 .28351 L .94677 .28235 L .95307 .28131 L .95929 .28029 L .96489 .27936 L .96996 .27853 L .97505 .27769 L .97968 .27693 L .98434 .27616 L .98861 .27545 L .99253 .27481 L .99651 .27415 L 1 .27358 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgI06JI09VI0IIIVJIIYVII/bII_nIIP3IVFJIVIVIVLbIVOnIV@3Ic6JIc9VIcI ofJIoiVIolbIoonIo`33Pl?3a0@414A4A8B4Qo`041?l001So00<4ool0 6Ol00`Coo`0Io`031?oo06Ko000Lo`D00_l00`3oo`06o`030?oo01So00<4ooh01Oh>o`D000?o1?l0 6_l00`Coo`0Io`031?oo01Wo00<4ool0I_l001ko00L0oooo0?l000Oo00<010@04`@7oPh40`1N16So 000No`070?ooo`3o0007o`030?oo00go1_h5o`031?oo00Go0`03o`803?l00`Coo`0Io`031?oo01Wo 00<4ool06Ol00`Coo`1Vo`007_l01`3oool0o`001ol00`3oo`07o`Kn2ol00`Coo`03o`805?l00`Co o`0Io`031?oo01Wo00<4ool06Ol00`Coo`1Vo`007_l01`3oool0o`001ol0103oool6oPko1@0Jo`03 1?oo01Wo00<4ool06Ol00`Coo`0Io`031?oo06Ko000Mo`801?l00`3oo`06o`Cn3_l300Ko00<4ool0 6Ol00`Coo`0Io`031?oo01Wo00<4ool06Ol00`Coo`1Vo`00;?l00`3oo`0=o`802Ol00`Coo`0Io`03 1?oo01Wo00<4ool06Ol00`Coo`0Io`031?oo06Ko000/o`030?oo00Go1@0>o`031?oo01Wo00<4ool0 6Ol00`Coo`0Io`031?oo01Wo00<4ool0I_l002co00<0o`000P0Fo`031?oo01Wo00<4ool06Ol00`Co o`0Io`031?oo01Wo00<4ool0I_l002co0P0Io`031?oo01Wo00<4ool06Ol00`Coo`0Io`031?oo01Wo 00<4ool0I_l002co00<0ool06?l00`Coo`0Io`031?oo01Wo00<4ool06Ol00`Coo`0Io`031?oo06Ko 000/o`030?oo01So00<4ool06Ol00`Coo`0Io`031?oo01Wo00<4ool06Ol00`Coo`1Vo`00;?l00`3o o`0Ho`031?oo01Wo00<4ool06Ol00`Coo`0Io`031?oo01Wo00<4ool0I_l002co00<0ool06?l00`Co o`0Io`031?oo01Wo00<4ool06Ol00`Coo`0Io`031?oo06Ko000/o`030?oo01So00<4ool06Ol00`Co o`0Io`031?oo01Wo00<4ool06Ol00`Coo`1Vo`00;?l00`3oo`0Ho`031?oo01Wo00<4ool06Ol00`Co o`0Io`031?oo01Wo00<4ool0I_l002co00<010@0R@AXo`00;?l00`3oo`0Ho`031?oo01Wo00<4ool0 6Ol00`Coo`0Io`031?oo01Wo00<4ool0I_l002co00<0ool06?l00`Coo`0Io`031?oo01Wo00<4ool0 6Ol00`Coo`0Io`031?oo06Ko000/o`030?oo01So00<4ool06Ol00`Coo`0Io`031?oo01Wo00<4ool0 6Ol00`Coo`1Vo`007_l00`3oo`02o`030?oo00Ko00<0ool06?l00`Coo`0Io`031?oo01Wo00<4ool0 6Ol00`Coo`0Io`031?oo06Ko000Mo`030?l000;o00<0o`001ol00`3oo`0Ho`031?oo01Wo00<4ool0 6Ol00`Coo`0Io`031?oo01Wo00<4ool0I_l001oo00H0ool0o`07o`030?oo01So00<4ool06Ol00`Co o`0Io`031?oo01Wo00<4ool06Ol00`Coo`1Vo`007Ol200?o00<0o`001ol00`3oo`0Ho`031?oo01Wo 00<4ool06Ol00`Coo`0Io`031?oo01Wo00<4ool0I_l001go00<0ool00_l00`3o0007o`030?oo01So 00<4ool06Ol00`Coo`0Io`031?oo01Wo00<4ool06Ol00`Coo`1Vo`007Ol300?o00<0ool01_l00`3o o`0Ho`031?oo01Wo00<4ool06Ol00`Coo`0Io`031?oo01Wo00<4ool0I_l002co00<0ool06?l00`Co o`0Io`031?oo01Wo00<4ool06Ol00`Coo`0Io`031?oo06Ko000/o`030?oo01So00<4ool06Ol00`Co o`0Io`031?oo01Wo00<4ool06Ol00`Coo`1Vo`00;?l00`3oo`0Ho`031?oo01Wo00<4ool06Ol00`Co o`0Io`031?oo01Wo00<4ool0I_l001Ko1@02o`030?oo00;o00<0ool01ol00`3oo`0Ho`031?oo01Wo 00<4ool06Ol00`Coo`0Io`031?oo01Wo00<4ool0I_l001So00L0oooo0?l000;o00<0o`002?l00`04 102916So000Ho`070?ooo`3o0002o`030?l00?co000Ho`070?ooo`3o0002o`030?l00?co000Ho`07 0?ooo`3o0002o`030?l00?co000Go`801?l00`3oo`02o`030?oo0?_o003oob7o003oob7o0005o`80 2ol00`3oo`0lo`030?oo0"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-3.5856, -2.55593, 0.0359338, 0.0348853}}] }, Open ]], Cell[CellGroupData[{ Cell["runtime = SessionTime[] - startclock", "Input"], Cell[BoxData[ \(12.0000000000000017`\)], "Output"] }, Open ]] }, FrontEndVersion->"4.0 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, WindowToolbars->{}, CellGrouping->Manual, WindowSize->{833, 566}, WindowMargins->{{2, Automatic}, {Automatic, 5}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, -1}}, ShowCellLabel->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, StyleDefinitions -> "AvpStyle.nb" ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{ "S5.63.1"->{ Cell[42577, 1471, 87, 1, 30, "Input", CellTags->"S5.63.1"], Cell[44867, 1557, 132, 4, 30, "Input", Evaluatable->False, CellTags->"S5.63.1"]} } *) (*CellTagsIndex CellTagsIndex->{ {"S5.63.1", 132225, 4555} } *) (*NotebookFileOutline Notebook[{ Cell[1717, 49, 74, 0, 64, "Subtitle"], Cell[CellGroupData[{ Cell[1816, 53, 42, 0, 34, "Text"], Cell[1861, 55, 41, 0, 70, "Input"], Cell[1905, 57, 39, 0, 70, "Input"], Cell[1947, 59, 44, 0, 70, "Input"], Cell[1994, 61, 36, 0, 70, "Input"], Cell[2033, 63, 37, 0, 70, "Input"], Cell[2073, 65, 38, 0, 70, "Input"], Cell[2114, 67, 38, 0, 70, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[2189, 72, 229, 4, 27, "Input"], Cell[2421, 78, 228, 5, 29, "Output"] }, Open ]], Cell[2664, 86, 433, 7, 69, "SmallText"], Cell[3100, 95, 63, 0, 53, "Section"], Cell[3166, 97, 230, 4, 50, "SmallText"], Cell[3399, 103, 32, 0, 47, "Subsection"], Cell[3434, 105, 120, 3, 31, "SmallText"], Cell[3557, 110, 188, 4, 31, "SmallText"], Cell[3748, 116, 285, 5, 84, "Input"], Cell[4036, 123, 69, 0, 31, "SmallText"], Cell[4108, 125, 51, 1, 30, "Input"], Cell[4162, 128, 70, 0, 30, "Input"], Cell[4235, 130, 213, 4, 66, "Input"], Cell[CellGroupData[{ Cell[4473, 138, 139, 3, 48, "Input"], Cell[4615, 143, 29324, 964, 186, 18395, 825, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[33954, 1110, 75, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[34054, 1114, 56, 0, 43, "Subsubsection"], Cell[34113, 1116, 113, 3, 30, "Input"], Cell[34229, 1121, 26, 0, 31, "SmallText"], Cell[34258, 1123, 40, 0, 30, "Input"], Cell[34301, 1125, 154, 3, 31, "SmallText"], Cell[34458, 1130, 176, 4, 48, "Input"], Cell[CellGroupData[{ Cell[34659, 1138, 72, 2, 30, "Input", Evaluatable->False], Cell[34734, 1142, 66, 1, 45, "Output"] }, Open ]], Cell[34815, 1146, 69, 0, 31, "SmallText"], Cell[34887, 1148, 196, 5, 30, "Input", Evaluatable->False], Cell[35086, 1155, 141, 3, 31, "SmallText"], Cell[CellGroupData[{ Cell[35252, 1162, 192, 4, 48, "Input"], Cell[35447, 1168, 148, 2, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[35632, 1175, 112, 2, 30, "Input"], Cell[35747, 1179, 194, 3, 53, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[35978, 1187, 210, 6, 84, "Input"], Cell[36191, 1195, 65, 1, 44, "Output"] }, Open ]], Cell[36271, 1199, 77, 0, 31, "SmallText"], Cell[CellGroupData[{ Cell[36373, 1203, 47, 1, 30, "Input"], Cell[36423, 1206, 78, 1, 52, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[36550, 1213, 67, 0, 43, "Subsubsection"], Cell[36620, 1215, 108, 3, 30, "Input"], Cell[36731, 1220, 76, 0, 31, "SmallText"], Cell[36810, 1222, 113, 3, 30, "Input"], Cell[36926, 1227, 192, 4, 48, "Input"], Cell[37121, 1233, 51, 0, 31, "SmallText"], Cell[CellGroupData[{ Cell[37197, 1237, 184, 4, 30, "Input", Evaluatable->False], Cell[37384, 1243, 156, 3, 41, "Output"] }, Open ]], Cell[37555, 1249, 262, 5, 50, "SmallText"], Cell[CellGroupData[{ Cell[37842, 1258, 76, 0, 31, "SmallText"], Cell[CellGroupData[{ Cell[37943, 1262, 65, 1, 30, "Input"], Cell[38011, 1265, 84, 1, 52, "Output"] }, Open ]], Cell[38110, 1269, 179, 3, 31, "SmallText"] }, Open ]], Cell[38304, 1275, 182, 4, 31, "SmallText"], Cell[38489, 1281, 93, 1, 30, "Input"], Cell[CellGroupData[{ Cell[38607, 1286, 59, 1, 30, "Input"], Cell[38669, 1289, 184, 3, 55, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[38890, 1297, 121, 2, 30, "Input"], Cell[39014, 1301, 194, 3, 53, "Output"] }, Open ]] }, Open ]], Cell[39235, 1308, 72, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[39332, 1312, 87, 2, 30, "Input"], Cell[39422, 1316, 208, 5, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[39667, 1326, 79, 1, 30, "Input"], Cell[39749, 1329, 55, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[39841, 1335, 50, 1, 30, "Input"], Cell[39894, 1338, 194, 3, 53, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[40125, 1346, 111, 2, 30, "Input"], Cell[40239, 1350, 173, 3, 53, "Output"] }, Open ]], Cell[40427, 1356, 110, 3, 31, "SmallText"], Cell[40540, 1361, 174, 7, 120, "Input"], Cell[CellGroupData[{ Cell[40739, 1372, 44, 1, 30, "Input"], Cell[40786, 1375, 54, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[40877, 1381, 35, 1, 30, "Input"], Cell[40915, 1384, 60, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[41012, 1390, 42, 1, 30, "Input"], Cell[41057, 1393, 58, 1, 44, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[41152, 1399, 35, 1, 30, "Input"], Cell[41190, 1402, 54, 1, 29, "Output"] }, Open ]], Cell[41259, 1406, 111, 3, 31, "SmallText"], Cell[CellGroupData[{ Cell[41395, 1413, 67, 0, 30, "Input"], Cell[41465, 1415, 75, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[41577, 1421, 45, 0, 30, "Input"], Cell[41625, 1423, 87, 1, 45, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[41749, 1429, 66, 0, 30, "Input"], Cell[41818, 1431, 61, 1, 29, "Output"] }, Open ]], Cell[41894, 1435, 42, 0, 53, "Section"], Cell[41939, 1437, 122, 3, 31, "SmallText"], Cell[42064, 1442, 32, 0, 47, "Subsection"], Cell[42099, 1444, 52, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[42176, 1448, 36, 0, 30, "Input"], Cell[42215, 1450, 266, 13, 212, "Print"] }, Open ]], Cell[42496, 1466, 56, 1, 30, "Input"], Cell[CellGroupData[{ Cell[42577, 1471, 87, 1, 30, "Input", CellTags->"S5.63.1"], Cell[42667, 1474, 73, 1, 42, "Output"] }, Open ]], Cell[42755, 1478, 392, 7, 130, "Input"], Cell[CellGroupData[{ Cell[43172, 1489, 174, 3, 30, "Input"], Cell[43349, 1494, 442, 7, 48, "Output"] }, Open ]], Cell[43806, 1504, 351, 7, 84, "Input"], Cell[44160, 1513, 71, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[44256, 1517, 35, 0, 30, "Input"], Cell[44294, 1519, 477, 30, 501, "Print"] }, Open ]], Cell[44786, 1552, 56, 1, 30, "Input"], Cell[CellGroupData[{ Cell[44867, 1557, 132, 4, 30, "Input", Evaluatable->False, CellTags->"S5.63.1"], Cell[45002, 1563, 61, 1, 42, "Output"] }, Open ]], Cell[45078, 1567, 399, 7, 130, "Input"], Cell[45480, 1576, 50, 1, 30, "Input"], Cell[45533, 1579, 232, 4, 50, "SmallText"], Cell[CellGroupData[{ Cell[45790, 1587, 308, 6, 50, "Input"], Cell[46101, 1595, 967, 13, 105, "Output"] }, Open ]], Cell[47083, 1611, 293, 6, 84, "Input"], Cell[47379, 1619, 101, 2, 31, "SmallText"], Cell[47483, 1623, 47, 1, 30, "Input"], Cell[47533, 1626, 72, 0, 30, "Input"], Cell[47608, 1628, 231, 5, 66, "Input"], Cell[CellGroupData[{ Cell[47864, 1637, 198, 4, 66, "Input"], Cell[48065, 1643, 35634, 1097, 186, 20769, 909, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[83714, 2743, 115, 3, 55, "Subsubtitle"], Cell[83832, 2748, 44, 0, 30, "Input"], Cell[83879, 2750, 79, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[83983, 2754, 56, 0, 43, "Subsubsection"], Cell[84042, 2756, 131, 3, 30, "Input"], Cell[84176, 2761, 31, 0, 31, "SmallText"], Cell[84210, 2763, 210, 5, 48, "Input", Evaluatable->False], Cell[84423, 2770, 26, 0, 31, "SmallText"], Cell[CellGroupData[{ Cell[84474, 2774, 218, 5, 30, "Input", Evaluatable->False], Cell[CellGroupData[{ Cell[84717, 2783, 68, 0, 30, "Input"], Cell[84788, 2785, 104, 2, 47, "Output"] }, Open ]], Cell[84907, 2790, 64, 0, 31, "SmallText"] }, Open ]], Cell[84986, 2793, 145, 3, 31, "SmallText"], Cell[85134, 2798, 187, 4, 48, "Input"], Cell[CellGroupData[{ Cell[85346, 2806, 55, 0, 30, "Input"], Cell[85404, 2808, 189, 3, 53, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[85630, 2816, 51, 0, 30, "Input"], Cell[85684, 2818, 101, 2, 52, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[85834, 2826, 67, 0, 43, "Subsubsection"], Cell[85904, 2828, 113, 3, 30, "Input"], Cell[86020, 2833, 98, 2, 31, "SmallText"], Cell[86121, 2837, 134, 3, 30, "Input"], Cell[86258, 2842, 156, 5, 66, "Input"], Cell[86417, 2849, 24, 0, 31, "SmallText"], Cell[86444, 2851, 418, 8, 50, "Input", Evaluatable->False], Cell[86865, 2861, 235, 4, 50, "SmallText"], Cell[87103, 2867, 184, 4, 31, "SmallText"], Cell[87290, 2873, 126, 2, 30, "Input"], Cell[CellGroupData[{ Cell[87441, 2879, 90, 1, 30, "Input"], Cell[87534, 2882, 325, 6, 47, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[87908, 2894, 88, 1, 30, "Input"], Cell[87999, 2897, 122, 2, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[88158, 2904, 91, 1, 30, "Input"], Cell[88252, 2907, 242, 4, 53, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[88531, 2916, 151, 3, 30, "Input"], Cell[88685, 2921, 183, 3, 53, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[88905, 2929, 55, 1, 30, "Input"], Cell[88963, 2932, 97, 2, 49, "Output"] }, Open ]], Cell[89075, 2937, 50, 0, 43, "Subsubsection"], Cell[89128, 2939, 142, 3, 31, "SmallText"], Cell[CellGroupData[{ Cell[89295, 2946, 204, 5, 48, "Input"], Cell[89502, 2953, 179, 3, 53, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[89718, 2961, 75, 1, 30, "Input"], Cell[89796, 2964, 79, 1, 49, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[89912, 2970, 133, 3, 30, "Input"], Cell[90048, 2975, 139, 2, 53, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[90224, 2982, 70, 1, 30, "Input"], Cell[90297, 2985, 177, 3, 53, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[90511, 2993, 66, 1, 30, "Input"], Cell[90580, 2996, 144, 2, 53, "Output"] }, Open ]], Cell[90739, 3001, 72, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[90836, 3005, 50, 0, 30, "Input"], Cell[90889, 3007, 215, 5, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[91141, 3017, 84, 1, 30, "Input"], Cell[91228, 3020, 58, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[91323, 3026, 54, 1, 30, "Input"], Cell[91380, 3029, 325, 6, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[91742, 3040, 91, 1, 30, "Input"], Cell[91836, 3043, 119, 2, 53, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[91992, 3050, 116, 2, 30, "Input"], Cell[92111, 3054, 255, 4, 47, "Output"] }, Open ]], Cell[92381, 3061, 110, 3, 31, "SmallText"], Cell[92494, 3066, 200, 10, 174, "Input"], Cell[CellGroupData[{ Cell[92719, 3080, 42, 1, 30, "Input"], Cell[92764, 3083, 64, 1, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[92865, 3089, 63, 0, 30, "Input"], Cell[92931, 3091, 75, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[93043, 3097, 45, 0, 30, "Input"], Cell[93091, 3099, 87, 1, 45, "Output"] }, Open ]], Cell[93193, 3103, 104, 2, 31, "SmallText"], Cell[CellGroupData[{ Cell[93322, 3109, 66, 0, 30, "Input"], Cell[93391, 3111, 61, 1, 29, "Output"] }, Open ]], Cell[93467, 3115, 47, 0, 31, "SmallText"], Cell[CellGroupData[{ Cell[93539, 3119, 63, 0, 30, "Input"], Cell[93605, 3121, 75, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[93717, 3127, 45, 0, 30, "Input"], Cell[93765, 3129, 87, 1, 45, "Output"] }, Open ]], Cell[93867, 3133, 104, 2, 31, "SmallText"], Cell[CellGroupData[{ Cell[93996, 3139, 66, 0, 30, "Input"], Cell[94065, 3141, 61, 1, 29, "Output"] }, Open ]], Cell[94141, 3145, 67, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[94233, 3149, 57, 1, 30, "Input"], Cell[94293, 3152, 56, 1, 29, "Output"] }, Open ]], Cell[94364, 3156, 229, 4, 50, "SmallText"], Cell[94596, 3162, 215, 4, 50, "SmallText"], Cell[94814, 3168, 52, 0, 31, "SmallText"], Cell[CellGroupData[{ Cell[94891, 3172, 124, 5, 84, "Input"], Cell[95018, 3179, 54, 1, 29, "Output"] }, Open ]], Cell[95087, 3183, 175, 3, 31, "SmallText"], Cell[95265, 3188, 108, 3, 31, "SmallText"], Cell[CellGroupData[{ Cell[95398, 3195, 154, 8, 138, "Input"], Cell[95555, 3205, 212, 4, 53, "Output"], Cell[CellGroupData[{ Cell[95792, 3213, 58, 1, 30, "Input"], Cell[95853, 3216, 54, 1, 29, "Output"] }, Open ]], Cell[95922, 3220, 70, 0, 31, "SmallText"], Cell[CellGroupData[{ Cell[96017, 3224, 62, 1, 30, "Input"], Cell[96082, 3227, 54, 1, 29, "Output"] }, Open ]], Cell[96151, 3231, 156, 3, 31, "SmallText"], Cell[CellGroupData[{ Cell[96332, 3238, 60, 1, 30, "Input"], Cell[96395, 3241, 54, 1, 29, "Output"] }, Open ]] }, Open ]], Cell[96476, 3246, 494, 13, 108, "Input"], Cell[96973, 3261, 495, 13, 108, "Input"], Cell[CellGroupData[{ Cell[97493, 3278, 338, 10, 79, "Input"], Cell[97834, 3290, 33317, 1228, 186, 22772, 1093, "GraphicsData", \ "PostScript", "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[131188, 4523, 53, 0, 30, "Input"], Cell[131244, 4525, 54, 1, 29, "Output"] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)